Cut the butter into cubes. Take half of the butter (½ cup or 133g) and place it in a large saucepan, then set it over medium heat and stir until melted.
When it begins to bubble, stir the butter every ten seconds or so until it bubbles and begins to foam. Once you see brown bits floating in the butter and a nutty aroma is released, immediately remove the pan from the heat.
Pour the butter into a bowl to stop the cooking process, making sure to get all the browned bits from the bottom of the pan. Immediately add in the other half of the cubed butter, whisking until completely melted. At this point, the butter should be cooled to room temperature—if still hot, place it in the fridge.
Add in the brown sugar and granulated sugar and whisk for 1-2 minutes until well combined, then beat in the eggs and vanilla extract.
Once the mixture is smooth, divide it equally between two large bowls (this will act as the base for the two cookie doughs).
To one bowl, fold in all of the cocoa cookie dough ingredients: 1 ¼ cups all-purpose flour, ¼ cup black cocoa powder, ½ teaspoon baking soda, and ½ teaspoon salt. Just before the flour is fully combined, add in the ¾ cup of chopped white chocolate and mix until there are no more streaks of flour left. Do not overmix.
In the other bowl, fold in all of the plain cookie dough ingredients: 1 ½ cups all-purpose flour, ½ teaspoon baking soda, and ½ teaspoon salt. Just before the flour is fully combined, add in the ¾ cup of chopped milk or semisweet chocolate and mix until there are no more streaks of flour left. Do not overmix.
Alternate scooping between each type of dough with a 1-ounce (2 tablespoon) cookie scoop until full, then roll each ball of dough between your hands and place onto a baking sheet lined with wax paper (no need to space them apart).1
Cover the tray with plastic wrap and refrigerate for at least 2 hours but up to 4-5 days. At this point, the cookie dough can be frozen.2 You can bake the cookies immediately, but they will spread more and have less flavor.
When ready to bake, preheat the oven to 375℉ and line a baking sheet with parchment paper.
Evenly space the cookie dough balls onto the baking sheet with a 2'' gap between each cookie. Bake for 10-12 minutes, rotating the tray halfway through.
Remove the cookies from the oven once the edges are golden brown and set, but do not overbake. The inside of the cookies should still be gooey and slightly raw, as they will continue to cook as they cool. Once out of the oven, sprinkle the cookies with flaky salt and allow to cool before serving.